Generation of large sequences of normal record values and maxima

Abstract

In our recent paper (2018), algorithms of generation of normal record values were developed. It was shown there that the developed algorithms are more efficient and speedy than all existing at that time algorithms of generation of normal record values. Presented in this paper algorithm 2.2 is the most efficient algorithm amongst the algorithms of the paper of Pakhteev and Stepanov. It allows to generate “large” sequences of record values (up to two billion record values). In the present paper, two algorithms of generation of normal maxima are proposed. One of the proposed algorithms is based on algorithm 2.2. It also allows to generate maxima of samples of “large” sizes. An algorithm of generation of record times in general continuous case is also proposed in the present paper.